Probability of Customers Exceeding Number Solution

STEP 0: Pre-Calculation Summary
Formula Used
Probability of Customers Exceeding Number = Mean_Arrival_Rate*Exceeded Number Queuing Theory/Mean_Service_Rate
Pex = λa*k/μ
This formula uses 4 Variables
Variables Used
Probability of Customers Exceeding Number - The Probability of Customers Exceeding Number is the probability of the number of customers in the system exceeding a certain number.
Mean_Arrival_Rate - Mean_Arrival_Rate is number of customers arriving per unit time.
Exceeded Number Queuing Theory - Exceeded Number Queuing Theory is the number that has been exceeded by the given number of customers in a queuing system.
Mean_Service_Rate - Mean_Service_Rate is the number of customers served per unit time.
STEP 1: Convert Input(s) to Base Unit
Mean_Arrival_Rate: 1800 --> No Conversion Required
Exceeded Number Queuing Theory: 13 --> No Conversion Required
Mean_Service_Rate: 2000 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Pex = λa*k/μ --> 1800*13/2000
Evaluating ... ...
Pex = 11.7
STEP 3: Convert Result to Output's Unit
11.7 --> No Conversion Required
FINAL ANSWER
11.7 <-- Probability of Customers Exceeding Number
(Calculation completed in 00.004 seconds)

Credits

Created by Suman Ray Pramanik
Indian Institute of Technology (IIT), Kanpur
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Verified by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
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13 Basics of Industrial Engineering Calculators

Single Exponential Smoothing
Go Smooth_Averaged_Forecast_for_Period_t = Smoothing Constant*Previous observed Value+(1-Smoothing Constant)*Previous Period Forecast
New Number in Simplex Table
Go New Number of Simplex Table = Old Number of Simplex Table-Key Row of Simplex*Key Column of Simplex/Key Number of Simplex
Expected Number of Customers in Queue
Go Expected Number of Customers in Queue = (Mean_Arrival_Rate^2)/(Mean_Service_Rate*(Mean_Service_Rate-Mean_Arrival_Rate))
Probability of Customers Exceeding Number
Go Probability of Customers Exceeding Number = Mean_Arrival_Rate*Exceeded Number Queuing Theory/Mean_Service_Rate
Number of Kanbans
Go No. of Kanban = (Demand_per_Year*Lead Time*(1+Safety_Factor))/Container Size
Expected Number of Customers in System
Go Expected Number of Customers in System = Mean_Arrival_Rate/(Mean_Service_Rate-Mean_Arrival_Rate)
Expected Length of Non-Empty Queue
Go Expected Length of Non-empty Queue = Mean_Service_Rate/(Mean_Service_Rate-Mean_Arrival_Rate)
Gross Margin Return on Investment
Go Return_on_Investment_(ROI) = Gross_Profit/((Opening Stock-Closing Stock)/2)*100
Perfect Order Measurement
Go Perfect Order Measurement = ((Total Orders-Error Orders)/Total Orders)*100
Uniform Series Present Sum of Money
Go Annual_Devaluation_Rate = Rate_of_Return_Foreign_Currency+Rate_of_Return_USD
Point r on Line
Go Point r on Line = Point a+Lambda*Point b
Non-Empty Queue Probability
Go Non-empty Queue Probability = (Mean_Arrival_Rate/Mean_Service_Rate)^2
Standard Error (Pooled)
Go Standard Error = (Mean Square Error^0.5)/Observations

Probability of Customers Exceeding Number Formula

Probability of Customers Exceeding Number = Mean_Arrival_Rate*Exceeded Number Queuing Theory/Mean_Service_Rate
Pex = λa*k/μ

What is Probability of customers exceeding a number?

The Probability of customers exceeding a number is the probability of the number of customers in the system exceeding a certain number. it is given as the product of the exceeded number and the ratio of the mean arrival rate to the mean service rate.

How to Calculate Probability of Customers Exceeding Number?

Probability of Customers Exceeding Number calculator uses Probability of Customers Exceeding Number = Mean_Arrival_Rate*Exceeded Number Queuing Theory/Mean_Service_Rate to calculate the Probability of Customers Exceeding Number, The Probability of Customers Exceeding Number is the probability of the number of customers in the system exceeding a certain number. Probability of Customers Exceeding Number is denoted by Pex symbol.

How to calculate Probability of Customers Exceeding Number using this online calculator? To use this online calculator for Probability of Customers Exceeding Number, enter Mean_Arrival_Rate a), Exceeded Number Queuing Theory (k) & Mean_Service_Rate (μ) and hit the calculate button. Here is how the Probability of Customers Exceeding Number calculation can be explained with given input values -> 11.7 = 1800*13/2000.

FAQ

What is Probability of Customers Exceeding Number?
The Probability of Customers Exceeding Number is the probability of the number of customers in the system exceeding a certain number and is represented as Pex = λa*k/μ or Probability of Customers Exceeding Number = Mean_Arrival_Rate*Exceeded Number Queuing Theory/Mean_Service_Rate. Mean_Arrival_Rate is number of customers arriving per unit time, Exceeded Number Queuing Theory is the number that has been exceeded by the given number of customers in a queuing system & Mean_Service_Rate is the number of customers served per unit time.
How to calculate Probability of Customers Exceeding Number?
The Probability of Customers Exceeding Number is the probability of the number of customers in the system exceeding a certain number is calculated using Probability of Customers Exceeding Number = Mean_Arrival_Rate*Exceeded Number Queuing Theory/Mean_Service_Rate. To calculate Probability of Customers Exceeding Number, you need Mean_Arrival_Rate a), Exceeded Number Queuing Theory (k) & Mean_Service_Rate (μ). With our tool, you need to enter the respective value for Mean_Arrival_Rate, Exceeded Number Queuing Theory & Mean_Service_Rate and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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